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Quasi-symmetric 2-(28, 12, 11) designs with an automorphism of order 7

✍ Scribed by Yuan Ding; Sheridan Houghten; Clement Lam; Suzan Smith; Larry Thiel; Vladimir D. Tonchev

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
142 KB
Volume
6
Category
Article
ISSN
1063-8539

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✦ Synopsis

All quasi-symmetric 2-(28, 12, 11) designs with an automorphism of order 7 without fixed points or blocks are enumerated. Up to isomorphism, there are exactly 246 such designs. All but four of these designs are embeddable as derived designs in symmetric 2-(64, 28, 12) designs, producing in this way at least 8784 nonisomorphic symmetric 2-(64, 28, 12) designs. The remaining four 2-(28, 12, 11) designs are the first known examples of nonembeddable quasisymmetric quasi-derived designs. These symmetric 2-(64, 28, 12) designs also produce at least 8784 nonisomorphic quasi-symmetric 2-(36, 16, 12) designs with intersection numbers 6 and 8, including the first known examples of quasi-symmetric 2-(36, 16, 12) designs with a trivial automorphism group.

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## Abstract We complete the classification of all symmetric designs of order nine admitting an automorphism of order six. As a matter of fact, the classification for the parameters (35,17,8), (56,11,2), and (91,10,1) had already been done, and in this paper we present the results for the parameters